Local-Fit Search for a Unidimensional Model

Searches for a specification of a one-factor model that reaches the fit targets, combining two actions — dropping items and freeing residual covariances — and then cleaning up the result.

Usage

local_fit_search(
  data,
  items,
  factor_name = "F",
  item_text = NULL,
  rmsea_target = 0.08,
  cfi_target = 0.95,
  srmr_target = 0.08,
  omega_min = 0.7,
  min_loading = 0.35,
  min_items = 5,
  max_ec = 4,
  mi_min = 5,
  start_ec = character(0),
  estimator = "WLSMV",
  ordered = TRUE,
  verbose = TRUE
)

Arguments

data: Data frame with the item responses.
items: Character vector of candidate item names.
factor_name: Name given to the latent variable. Default "F".
item_text: Optional data frame with columns Item and Texto (or Text); used only to print the wording of the items involved in each retained covariance, so that its substantive plausibility can be judged.
rmsea_target, cfi_target, srmr_target: Fit targets. Defaults 0.08, 0.95 and 0.08.
omega_min: Reliability floor. Default 0.70.
min_loading: Loading floor. Default 0.35.
min_items: Minimum number of retained items. Default 5.
max_ec: Maximum number of residual covariances. Default 4.
mi_min: Minimum modification index for a covariance to be considered. Default 5.
start_ec: Character vector of residual covariances to start from, in lavaan syntax (e.g. "IT1 ~~ IT2"). Default none.
estimator, ordered: Passed to cfa.
verbose: Logical; print progress. Default TRUE.

Value

An object of class local_fit_search, a list with best (the retained model and its indices), log (one row per action, with its phase), ec_detail (the retained covariances with sign, interval and wording), meets and config.

Details

Applies to the scale that is essentially unidimensional but whose one-factor model misfits. Where redundancy_short_form attacks a single cause (local dependence between near-duplicate items) by pruning, this routine also considers keeping the pair and modelling its residual covariance, and decides between the two by their effect on fit.

Four phases, three of which encode decisions usually taken by hand.

Phase 0 — sanitation. Items below the loading floor are removed without requiring that fit improve. An item that does not load cannot stay, and dropping it often worsens RMSEA temporarily because the degrees of freedom lost outweigh the chi-square gained. A rule that demanded immediate improvement would reject the removal and stall the search before it starts.

Phase 1 — greedy search. At each step both actions are evaluated for every candidate — drop an item, or free one residual covariance — and the one that most reduces RMSEA is taken.

Phase 2 — consolidation. If an item takes part in two or more residual covariances, the item is the problem and not the relations: dropping it is attempted, which typically resolves both at once and buys back a degree of freedom.

Phase 3 — parsimony. Each retained covariance is removed in turn; those that are not needed to keep meeting the targets are discarded. Every freed parameter is a debt that has to be justified.

What the function does not do is judge whether a covariance makes substantive sense. It returns its estimate, confidence interval, sign and — when item_text is supplied — the wording of both items, so that decision stays with whoever knows the construct. A negative residual covariance between items at opposite poles of a construct is often the trace of a dimension that the unidimensional model absorbed, and is worth reading before treating it as noise.

Warning. This is a data-driven search and capitalises on chance (MacCallum, Roznowski & Necowitz, 1992). It establishes whether an admissible specification exists; it does not replace validation on an independent sample.

References

MacCallum, R. C., Roznowski, M., & Necowitz, L. B. (1992). Model modifications in covariance structure analysis: The problem of capitalization on chance. Psychological Bulletin, 111(3), 490-504.

Saris, W. E., Satorra, A., & van der Veld, W. M. (2009). Testing structural equation models or detection of misspecifications? Structural Equation Modeling, 16(4), 561-582.

Examples

# \donttest{
data(Data_Expectativas)
res <- local_fit_search(Data_Expectativas, paste0("EAF", 1:10),
         factor_name = "Expectations", estimator = "MLR", ordered = FALSE)
#> 
#> [start] n=10 ec=0 | CFI=0.838 RMSEA=0.121 omega=0.851 min_loading=0.419
#> 
#> == Phase 0: sanitation (items below the loading floor) ==
#>    every loading reaches the floor
#> 
#> == Phase 1: greedy search (drop item / add covariance) ==
#>    drop EAF6                n= 9 ec=0 | CFI=0.906 RMSEA=0.097
#>    drop EAF5                n= 8 ec=0 | CFI=0.975 RMSEA=0.055
#>    targets reached
#> 
#> == Phase 2: consolidation (item in 2+ covariances) ==
#>    nothing to consolidate
#> 
#> == Phase 3: parsimony (remove dispensable covariances) ==
#>    no covariances
res
#> 
#> Local-Fit Search
#> ----------------------------------------------------------
#> Solution: 8 items, 0 covariance(s) | MEETS the targets
#>   chi2(20) = 26.1 | CFI = 0.975 | TLI = 0.965 | RMSEA = 0.055 | SRMR = 0.045
#>   omega = 0.875 | minimum loading = 0.580
#>   Items: EAF1, EAF2, EAF3, EAF4, EAF7, EAF8, EAF9, EAF10 
#> 
#> Data-driven search: cross-validate on an independent sample.
res$log
#>       phase    action n_items n_ec   cfi   tli rmsea  srmr omega meets
#> 1  0. start     start      10    0 0.838 0.791 0.121 0.090 0.851 FALSE
#> 2 1. search drop EAF6       9    0 0.906 0.875 0.097 0.067 0.868 FALSE
#> 3 1. search drop EAF5       8    0 0.975 0.965 0.055 0.045 0.875  TRUE
# }